The existing manufacturing technologies for semiconductor integrated circuits and flat panel displays may include processing of silicon wafers and glass panels, often referred to as substrates, in fully automated vacuum cluster tools, which may utilize robotic manipulators to cycle the substrates through individual stations and operations performed in the tools.
The robotic manipulators typically hold the substrate subject to processing by means of frictional force between the substrate and the robot end-effector. The force may be supplemented by a vacuum or electrostatic hold-down in some applications. Since the inertial force at the substrate must not exceed the holding force securing the substrate to the end-effector in order to prevent undesirable slippage, the acceleration of the substrate must be limited accordingly. Additional constraints, such as limited velocity and jerk, are typically required for safe operation and trajectory tracking reasons. For maximum throughput levels, an efficient method for calculating a substrate transfer trajectory without causing the substrate carried by the robotic manipulator to slide, and without violating other prescribed constraints, may be required.
Conventional methods in the area of time-optimum trajectory may include a number of algorithms which can potentially be applied or extended to the above applications. Conventional trajectory generation algorithms for transporting a substrate with a support typically take into account the acceleration components in the plane of operation of the arm of the robotic manipulator but may fail to consider the effects of vertical acceleration and deceleration that often takes place, e.g., during rotational moves of the robotic manipulator as the height of the arm of the robotic manipulator needs to adjust to different elevations of the stations in the tool. This may result in non-uniform slippage margins and suboptimal throughput performance. The slippage margins are further eroded due to vertical oscillations of the robot end-effector, which is often excited by vertical moves. In addition, the trajectories for the moves in the plane of operation of the arm of the robotic manipulator may have high frequency content, which requires high controller bandwidth for acceptable tracking.
In summary, conventional trajectory generation algorithms for transporting a substrate with a support may suffer from one or more of the following deficiencies: (1) Trajectories for rotary (T-axis) and vertical (Z-axis) moves may not be fully synchronized. The trajectories may start substantially at the same time, but their durations may generally be different. A Z-axis move may finish earlier than the simultaneous T-axis move, meaning that an unnecessarily high Z-axis acceleration and/or deceleration may be used. This may unnecessarily reduce the frictional force available to hold the substrate and may cause more end-effector vibration, which may further reduce the available frictional force. A T-axis move may finish earlier than the simultaneous Z-axis move. This may result in the substrate being subject to unnecessarily high acceleration force in the plane of operation of the arm of the robotic manipulator, i.e., in the plane of the end-effector. This may unnecessarily reduce the slippage margin, (2) T-axis trajectories do not take into account acceleration and deceleration effects of the Z-axis which may affect the frictional force available to hold the substrate. T-axis moves have a reduced slippage margin when the available frictional force is reduced due to acceleration or deceleration of the Z-axis. This occurs in the deceleration phase of upward Z-axis moves and acceleration phase of downward Z-axis moves. T-axis moves are slower than they can be when the available frictional force is increased due to acceleration or deceleration of the Z-axis. This occurs in the acceleration phase of upward Z-axis moves and deceleration phase of downward Z-axis moves. (3) The frictional force available to hold the substrate and, therefore, the slippage margin may be reduced due to vibration of the robot end-effector which may be excited by execution of a Z-axis trajectory. (4) The trajectories for the moves in the plane of operation of the arm of the robotic manipulator may have high frequency content which may require high bandwidth of the motion controller to achieve acceptable tracking errors. This may lead to closed-loop stability issues, particularly in direct-drive robotic manipulators.